Question

c= 1 + 2 mu 1 + 2 mu 2 + 2 mu 3 + .................. +2 2018

Answer 1

C = 1 + 2¹ + 2² + 2³ + ... + 2²⁰¹⁸

2C = 2¹ + 2² + 2³ + ... + 2²⁰¹⁸ + 2²⁰¹⁹

2C - C = C = ( 2¹ + 2² + 2³ + ... + 2²⁰¹⁸ + 2²⁰¹⁹) - ( 1 + 2¹ + 2² + 2³ + ... + 2²⁰¹⁸ )

C = 2²⁰¹⁹ - 1

Answer 2

\(C=1+2^1+2^2+2^3+2^4+.....+2^{2018}\)

\(\Leftrightarrow2C=2+2^3+2^4+2^5+....+2^{2019}\)

\(\Leftrightarrow2C-C=\left(2+2^{2019}\right)-\left(1+2^2\right)\)

\(\Leftrightarrow C=2+2^{2019}-2-2^2\)

\(\Leftrightarrow C=2+2^{2019}-5\)

\(\Leftrightarrow C=2^{2019}-3\)

Vậy : \(A=2^{2019}-3\)